MATH 401 Midterm: MATH 400 2005 Winter Test 1
Document Summary
Be sure that this examination has 7 pages. Write your name on top of each page. Submit only this booklet, with solution written in space provided (you may use adjacent page(s)). Solutions on scratch paper will not be graded. A 2-sided self-prepared letter-size formula sheet is allowed. In case of an exam disruption such as a re alarm, leave the exam papers in the room and exit quickly and quietly to a pre-designated location. Find the solution y(x, t) of the nonlinear pde problem yt + (1 3y2)yx = 0 < x < + , t > 0 y(x, 0) = p2/3, x < 0; x > 0. Consider a 2-dimensional problem in polar coordinates: utt(r, , t) = c2 u(r, , t), 0 < r < a, 0 /6, t > 0; (1) u(a, , t) = u(r, 0, t) = u(r, /6, t) = 0, u(r, , 0) = f (r, ), ut(r, , 0) = 0.
